They certainly do compete with each other but it's just a general misconception that competition lowers prices.
Pepsi and Coke have been competing with each other for decades and Coke has larger market share. So why doesn't Pepsi just lower prices? Pepsi even has the diversified income of doing more than drinks. Lowering prices doesn't lead to market share and Coke can just match the price.
Look at Apple's growth in the American market, they can sell a product that is significantly more expensive than competitors and still gain market share.